Iterative method, for making stochastic numerical model of Gaussian or arranged type, e.g. in hydrocarbon exploration, involves combining first Gaussian white noise associated with tolerance of pseudo-data with second Gaussian white noise

摘要

The local static data are transformed into point pseudo-data using the laws of probability and a spatial variability model. The pseudo-data are adjusted, maintaining the laws of probability and the spatial variability model, by the slope of an iterative process where one combines a first Gaussian white noise associated with the tolerance of the pseudo-data with a second Gaussian white noise : The distribution of a physical property in a porous heterogeneous medium is adjusted with respect to dynamic data, characteristic of fluid displacement in the medium, and local static data measured at a certain number of measuring points along a hole through the medium, with a certain margin of error. The model is optimized by the gradient of an iterative deformation process where at each iteration a combined result is formed by linear combination of the initial version, representing at least part of the medium and at least one second independent version of the same stochastic model. An objective function measuring the space between the real dynamic data and the dynamic data simulated by a flow simulator is minimized, for the combined result, adjusted by combination coefficients. The iterative adjustment process is pursued until an optimal version of the stochastic model is obtained. The model is adjusted by a gradual process by assuming that the sum of the squares of the combination coefficients between the results is 1 and the pseudo-data is adjusted by an iterative process where the sum of the squares of the coefficients of the combination is also 1. The laws of probability are normal or uniform laws. The iterative adjustment start with two deformation parameters, a first parameter which controls the combination of the initial version and a second parameter which controls the combination of the initial and second Gaussian white noises. Alternatively, the optimization is carried out from a single coefficient when the combination coefficients are identical to the combination of versions and white noises, or by a pilot point method.